2020/09/16 by Mihail Hurmuzov, Hurmuzov, Mihail
Mathematics · #05E45 (Secondary) #55N30 (Primary) 55T05 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2009.07665
openalex publication_date 2020/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop a bundle theory of presheaves on small categories, based on similar work by Brent Everitt and Paul Turner. For a certain set of presheaves on posets, we produce a Leray-Serre type spectral sequence that gives a reduction property for the cohomology of the presheaf. This extends the usual cohomological reduction of posets with a unique maximum.